Making joints between materials as dissimilar as metals and ceramics generally requires high temperature joining methods such as brazing or diffusion bonding. When such a joint is cooled to a lower temperature for use or for later manufacturing processes, stresses inherently develop within the joined materials. This occurs because the higher coefficient of thermal expansion material near the joint is precluded, by being joined to a lower coefficient of thermal expansion material, from contracting as much as would be expected from the temperature change. The bond forces the two joined materials to retain the same dimension along the area of the joint. Therefore, the joined material having the lower coefficient of thermal expansion develops a compressive stress in the interior of the joint and a tensile stress near the bond terminus of the joint.
Quantification of the stress patterns in a joint can be obtained by the established method of finite element analysis, hereinafter referred to as "FEA." A standard reference work for this method is O. C. Zienkiewicz, The Finite Element Method, 3rd Ed., McGraw Hill, London, 1977. Computer programs are available commercially for efficient practice of FEA. An example of such a program is ANSYS.TM. leased by Swanson Analysis Systems, Inc., Houston, Pa.
FEA involves calculating the mechanical characteristics of actual bodies by a series of approximations, in each of which the actual body is treated as if it were divided by a "mesh" into distinct elements. The behavior of the entire body is then determined by summing the contributions of the individual elements. Such calculations are performed with successively finer mesh sizes until the values reach a finite value without changing, within a predetermined tolerance limit, as the mesh size is made finer, or else grow ever larger as the mesh size is made finer. The latter behavior is described in the art as "singular" or "a singularity" and the former as convergent or finite.
If a material is made of a high quality single crystal without significant surface damage, or if the material is ductile, as are most metals, its mechanical properties will normally be highly consistent from sample to sample and will be determined by the strength of the chemical bonds in the material. In the more usual case of a brittle polycrystalline material, or even of single crystal material with less than meticulous surface preparation, the MOR will be less precisely reproducible and will be lower on average than for a flawless single crystal of the same nominal chemical composition. The difference arises from microscopic irregularities or flaws present at almost any interface, including the external surface and the numerous internal interfaces in the interior of polycrystalline materials. Brittle materials are known to behave as if rupturing forces were concentrated at flaws rather being uniformly distributed over the entire stressed area of the material.
The stress required to rupture practical non-ductile polycrystalline materials often show a wide statistical fluctuation, but for reproducibly prepared materials, fairly consistent failure statistics can be obtained, and they serve as an adequate guide to engineering design with the materials involved. One of the most often used methods of statistically treating the variability of the modulus of rupture is given by W. Weibull, "A Statistical Theory of the Strength of Materials," Ingeniors Handl. (Proceedings of the Royal Swedish Institute for Engineering Research), No. 151, 1939. This method allows calculation of a probability of failure for an object made of a specified material, given the distribution of stresses in the object and certain statistical parameters designated as the Weibull modulus and the characteristic strength of the material.
Metal to ceramic joints with the metal tapered at the bond terminus or edge of the joint have been occasionally used in the prior art, apparently on an empirical basis. In addition, ceramics and metals have been tapered in a matching fashion such that the tapered ceramic surface fits inside a tapered metal surface and is joined thereto (U.S. Pat. No. 4,679,960, Mizuhara). However, no prior use of ceramic to metal joints with the ceramic tapered away from the bond terminus and wherein the tapered surface is not bonded to the metal is known to applicants.